I don’t think of myself as a cooperator or defector; I consider myself to be one who (edit: tries to) cooperates if my opponent cooperates and defects if my opponent defects.
So, if the name changes, that can change what I expect others to do, and thus what I find that I should do.
It’s not clear how much of the effect is itself that—the expectation that others will see it differently. I wonder what would happen if you told the two players different things as to what the name of the game was, and then told one or the other player—or both—what the other player had been told the game would be.
Concerning game name changes:
I don’t think of myself as a cooperator or defector; I consider myself to be one who (edit: tries to) cooperates if my opponent cooperates and defects if my opponent defects.
So, if the name changes, that can change what I expect others to do, and thus what I find that I should do.
It’s not clear how much of the effect is itself that—the expectation that others will see it differently. I wonder what would happen if you told the two players different things as to what the name of the game was, and then told one or the other player—or both—what the other player had been told the game would be.